Nonlinear Wave Propagation in Fluid Flows

该项目旨在提高对外部扰动在深水表面产生波浪的基本认识。感兴趣的物理状态是当波的波长为几厘米时；重力和毛细效应都变得重要，波速达到定义临界强迫速度的最小值：以等于该最小速度的速度行进的外部强迫的线性响应随时间增长无界，并且，除了阻尼之外，非线性效应在这种共振附近可能变得重要。理论模型将用来研究强迫、非线性和阻尼力对共振条件下波浪响应的相互作用。理论预测将与文献中报道的实验室实验观测结果进行比较。重力毛细波的共振强迫与风在海洋表面产生的涟漪有关，表现为海洋表面的小尺度粗糙度，以及与小物体在自由表面上运动有关的波浪阻力。更广泛地说，这个问题是在有限波长具有最小相速的共振强迫波动系统的典型，其他潜在的应用包括漂浮的冰盖对水面飞行器的响应。

This project aims at improving the fundamental understanding of the generation of waves on the surface of deep water by an external disturbance. The physical regime of interest is when the waves have wavelength of a few cm; both gravity and capillary effects then become important, and the wave speed attains a minimum value which defines a critical forcing speed: the linear response to external forcing traveling with speed equal to this minimum grows unbounded with time and, apart from damping, nonlinear effects can become important near this resonance. Theoretical models will be used to study the interplay of forcing, nonlinear and damping effects on the wave response under resonant conditions. The theoretical predictions will be compared with laboratory experimental observations reported in the literature.Resonant forcing of gravity-capillary waves is relevant to the generation of ripples by wind, that appear as small-scale roughness on the ocean surface, and to the wave drag associated with the motion of small bodies on a free surface. More generally, this problem is prototypical of resonantly forced wave systems with a phase-speed minimum at finite wavelength, and other potential applications include the response of floating ice sheets to surface vehicles.